PIRSA:13100082 Scientific Series Quantum Fields and Strings

DOI10.48660/13100082

Series: Quantum Fields and Strings

Nakayama, Y. (2013). Vector Beta Function. Perimeter Institute. https://pirsa.org/13100082

Nakayama, Yu. Vector Beta Function. Perimeter Institute, Oct. 17, 2013, https://pirsa.org/13100082 

@misc{ pirsa_PIRSA:13100082,
  doi = {10.48660/13100082},
  url = {https://pirsa.org/13100082},
  author = {Nakayama, Yu},
  keywords = {Quantum Fields and Strings},
  language = {en},
  title = {Vector Beta Function},
  publisher = {Perimeter Institute},
  year = {2013},
  month = {oct},
  note = {PIRSA:13100082 see, \url{https://pirsa.org}}
}

Abstract

We propose various properties of renormalization group beta functions for vector operators in relativistic quantum field theories. We argue that they must satisfy compensated gauge invariance, orthogonality with respect to scalar beta functions, Higgs-like relation among anomalous dimensions and a gradient property. We further conjecture that non-renormalization holds if and only if the vector operator is conserved. The local renormalization group analysis guarantees the first three within power counting renormalization. We verify all the conjectures in conformal perturbation theories and holography in the weakly coupled gravity regime.

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